# Miller cylindrical projection

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The Miller cylindrical projection is a modified Mercator projection, proposed by Osborn Maitland Miller in 1942. The latitude is scaled by a factor of 45, projected according to Mercator, and then the result is multiplied by 54 to retain scale along the equator. [1] Hence:

## Contents

{\displaystyle {\begin{aligned}x&=\lambda \\y&={\frac {5}{4}}\ln \left[\tan \left({\frac {\pi }{4}}+{\frac {2\varphi }{5}}\right)\right]={\frac {5}{4}}\sinh ^{-1}\left(\tan {\frac {4\varphi }{5}}\right)\end{aligned}}}

or inversely,

{\displaystyle {\begin{aligned}\lambda &=x\\\varphi &={\frac {5}{2}}\tan ^{-1}e^{\frac {4y}{5}}-{\frac {5\pi }{8}}={\frac {5}{4}}\tan ^{-1}\left(\sinh {\frac {4y}{5}}\right)\end{aligned}}}

where λ is the longitude from the central meridian of the projection, and φ is the latitude. [2] Meridians are thus about 0.733 the length of the equator.

In GIS applications, this projection is known as: "ESRI:54003 - World Miller Cylindrical" [3]

Compact Miller projection is similar to Miller but spacing between parallels stops growing after 55 degrees. [4]

## Related Research Articles

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## References

1. Flattening the Earth: Two Thousand Years of Map Projections, John P. Snyder, 1993, pp. 179, 183, ISBN   0-226-76747-7.
2. "Miller Cylindrical Projection". Wolfram MathWorld. Retrieved 25 March 2015.
3. "Projected coordinate systems". ArcGIS Resources: ArcGIS Rest API. ESRI. Retrieved 16 June 2017.